Most existing types of the rotary positive displacement pumps and flowmeters have many moving parts, which have complex shapes and, consequently, they are not suitable or ideal for the construction of a pump or flowmeter of small size or those capable of measuring low volume flow rates. With few exceptions, the existing rotary positive displacement pumps or flowmeters employ a plurality of vanes or flaps included in a rotor assembly eccentrically disposed within a cavity in a rotatable arrangement. Since many moving parts are assembled into a single rotor assembly, firstly higher friction resulting from the movement of the individual parts make the existing rotary positive displacement flowmeter incapable of measuring low flow rates of fluids and, secondly, they are not suitable for construction into a pump or flowmeter of small size. These difficulties associated with the existing rotary positive displacement pump or flowmeter can be eliminated by employing a design including a single sliding rotor or vane disposed in a cavity wherein the sliding rotor or vane divides the cavity into two compartments during all phases of rotation thereof about an axis of rotation eccentric to the geometrical central axis of the cavity.